Resistance networks with thermistors



April 1952 EIJIRO TAKAGISHI 3,028,756

RESISTANCE NETWORKS WITH THERMISTORS Filed July 26, 1960 FIG and electrical source FIG 2 He 3 F e 7 R C '9'" .9. -Z (Pp) (Re) 0 ,7 a)

deviation of thermistor resistance F IG 4 deviation of thermistor resistance INVENTOR. [/J/PO T/I/(A C /S/H United States Patent I 3,028,756 RESISTANCE NETWORKS WITH THERMISTORS Eijiro Takagishi, 893 Kamikitazawa 3-chome, Setagaya-ku, Tokyo, Japan Filed July 26, 1960, Ser. No. 45,372 4 Claims. (Cl. 73-362) This invention relates to 'a resistance network with thermistor and particularly to a system for providing substantially definite temperature-resistance characteristics of a resistance network including a thermistor and a measuring instrument, irrespective of substantial deviation of the thermistor from its rated resistance value.

In the contemporary art of thermistor manufacture, it is substantially impossible to keep deviations of resistance values of thermistors within say il% in large scale production.

Even with -I% deviations or so, it is substantially impossible to provide substantially definite temperatureresistance characteristics of a resistance network including a thermistor, irrespective of change in its deviation. That is, the thermistor of a particular network can not have interchangeability. Consequently, when the thermistor of a particular resistance network associated with a measuring instrument, such as a' precision thermometer, wind velocity meter, temperature, regulating apparatus, etc., is spoiled and a new one should be used in place of the former, it is necessary for the user to send the whole apparatus including the measuring instrument to the factory where the whole apparatus should be reassembled, and re-adjusted or recalibrated murder to obtain an acceptable measuring, regulating or similar apparatus. I

There is, in addition, an inherent obstruction to -a large scale production of apparatus utilizing thermistors, because every apparatusshould individually be adjusted and calibrated, and'standardization is impossible even for the measuring instruments. T 1

It is an object of the present invention to provide substantially definite temperature-resistance characteristics of a resistance network including a-thermistor and a measuring instrument, irrespective of deviation of the thermistor, and consequently to enable to standardize the measuring instrument included in the network. I

Another object of the present invention 'is to provide a system for determining values of resistors constituting a network including a thermistoras well as a measuring instrument so that the thermistor deviation are compensated for, or the network may have definite temperatureresistance characteristics irrespective of deviation of the thermistor at three spaced definite points of difierent temperatures. definite points of different temperatures, it is substantially definite over the corresponding temperature range.

Another object of the present invention is to provide thermistor-probes that may consistently be associated with and operate in aproper manner for one and the samemeasuring instrument, irrespective of deviations of thermistors employed in the probes.

Other objects and particularities of the present invention will be made obvious from the following description of the constructional features of the present invention given with reference to the accompanying drawings,

wherein:

If a characteristic curve passes three spaced FIG. 1 is a block diagram representing the present I invention;

FIG. 2 shows conditions satisfied by the present invention;

FIG. 3 is a circuit diagram of the resistor network with athermistor;

.is shown in FIG. 3 as an example.

FIG. 4 shows values of resistors shown in FIG. 3 with reference to deviations of the thermistor resistance;

FIG. 5 shows a condition to be satisfied for embodying the present invention.

Referring to FIG. 1, the present invention comprises a thermistor 1, a resistor network 2 having a pair of terminals 3, and a measuring instrument with electrical source 4 connected across the terminals 3. The thermistor 1, network 2 and measuring instrument with electrical source are connected together in cascade. According to the present invention, by formulatingresistance values of respective resistors constituting the network 2 in a proper manner as hereinafter discussed in detail, the resultant resistance R of network 2 with thermistor 1 across terminals 3 can have definite values at three spaced definite points of different temperatures of thermistor 1, irrespective of deviations of the thermistor resistance from the rated value. In other words, resultant resistances Tia, En and Em, the values of 'E at temperatures T0, Tn and Tm, respectively, are fixed to respective predetermined values, in spite of changes in deviations of the thermistor resistance, where To Tn Tm. When three resultant resistances E0, in and fim are definite at three spaced definite points of temperatures To, Tn and Tm, respectively, it is deemed that a temperature-resistance curve passing such three points simultaneously is substantially definite, or the temperatureresistance characteristics of the particular network is substantially definite irrespective of changes in deviations of the thermistor 1.

It is known that the resultant resistance E0 can readily be fixed to a definite value at a temperature To irrespective of the resistance value R0 of thermistor 1 at that temperature, by proper selection of parallel and series resistor elements forming the network 2. Curve Ito in FIG. 2 illustrates such a condition. The number of possible combinations of resistor elements for satisfying such a condition is countless, and among them, one can readily choose a particular combination that satisfies another condition for fixing the resultant resistance fin at another temperature Tn to another definite value, irrespective of the resistance value Rn of thermistor 1 at that temperature, as shown by curve fin in'FIG. 2.

It is not easy, however, to obtain a definite resistance value Fm (FIG. 2) at the third temperature Tm irrespective of the resistance value Rm of thermistor 1 at temperature Tm by use of the same resistor combination that satisfies the first and second conditions, without teaching of the present invention. As far as I know, there has been no proposal practised for accomplishing such a result.

The resistor network 2 may have various forms comprising parallel and series resistors. A T-type network Aso-called wr-type network (not shown) is another example. While the present invention is explained below with reference to a T-type network shown in FIG. 3, it will be understood the principle disclosed thereby may readily be applied to a vr-type network with necessary and apparent changes.

Referring to FIG. 3, the network 2 comprises a pair of series resistors -7 and 8, and a parallel resistor 9 which is connected acrosathe thermistor 1 in series with resistor 7. The resistance values of these resistors are represented by Rp, Rp and Rq, respectively. Then, we can have the following obvious equations at temperatures To, Tn

and Tm, respectively:

Where n=Fo/R'n "m=R'0/Fm We then obtain the following equations:

q: l.i 4

En l) v=u-x If Equations 4, and 6 are substituted in the right sides of Equations 1, 2 and 3, both sides of Equations 1, 2 and 3 become equal, respectively. Then, it is understood that, in order to obtain definite values of F0, in

- and Em at respective temperatures To, Tn and Tm, ir-

respective of R0, Rn and Rm, the conditions represented by Equations 4, 5 and 6 must be satisfied simultaneously. Since p and p must, of course, be positive real numbers, weknow from Equations 5 and 6 that 7 I Rn must satisfy the following condition:

Rn(N)Rn S Rn(x) (7 Where I Rn(N) =the lower permissible limit of- Rn v-v W Rn(a:) =the upper permissible limit of Rn We may assume that a measure of the range within which the compensation of thermistor resistance deviations is properly obtained is In order to accomplish the required compensation,

\/p must be larger than unity, and the following condition is established from Equations 9 and 10:

. u u 5 x (11) Thus, I have obtained the conditions for keeping E0, in and Tim to respective definite values *atthree points of temperatures To, Tn and Tm, respectively, irrespective I of certain degrees of deviations of thermistor resistance from the rated values as follows: 7

(a) The functions of ratios of resultant resistances (5 and i) must satisfy the condition 11. I r

(b) The ratio of resultant resistance'to thermistor resistance (Rn/Rn) must satisfy the condition 7.

In other words, I have found that, with a given ther- V mistor, if T50, Fri and Tim are determined optionally, the

desired three point compensation cannot be accomplished at any. precise adjustment of the resistor combination of network 2. According to the invention, the above-mentioned two conditions a and b are satisfied for the resultant resistances F0, in and Tim, and the desired three point compensation is obtained consistently.

, After the resultant resistances E0, fin and Em at three points of temperatures To, Tn and Tm are determined as above-discussed, the respective resistances Rp, R'p and Rq of resistors 7, 8 and 9 are determined according to the deviation of the particular thermistor, from Equations 4, 5 and 6. A manner in which Rp,' Rp and Rq must be changed in accordance with deviations of thermistor resistance is shown in FIG. 4. I

The above-mentioned condition a may more easily be understood by the explanation given below.

Let me establish the following definition: F,=the ratio of the resultant resistance, of network 2 across thermistor 1, when terminals 3 are short circuited, to R0. Th a By substituting Equations 4, 5 and 6 in Equation 12,

then

Then, from Equations 9 and 10 :where From Equations 17 and 18, it is obvious that n and m have maximum values, respectively, for a certain value of F. In other Words, S n and m have upper permissible values, respectively. r In addition, by eliminating F from Equations 17 and 12 for obtaining the relation between (n1) and (Sm-l) with /7a as the parameter, I have obtained a closed loop curve as shown in FIG. 5. As \/p increases its value, the loop becomes smaller. It is then obvious that the desired three point compensation can be directed only within the area represented by the closed loop. In other words, the locus curve of FIG. 5 depicted by Equations 17 and 18 is a representation of the condition a in another expression, and this explains the reason why the three point compensation has heretobefore been extremely ditficult to be effected, though not impossible.

Next, I will give practical examples of apparatus embodying the present invention.

When thermistor 1 has a rated characteristic of R0=1.0 kilo-ohm, Rn= /z kilo-ohm, and

kilo-ohm According to the condition a, I select ZE=0.60(F==1.0) p=1.05/Q.95

' Hill-i! From the above equation, I obtain This satisfies the condition a By the definition,I obtain Then Rn(x) From the definitions Thus, all the three resultant resistances have been determined. v

The values to be afiorded to p, p and q for obtaining these resultant resistance values are obtained by Equations 4, 5 and 6, thus q=0.05008, p=0.5188, and p'-=0.4928

Table l Thermistor Deviation (percent) 0. 05 0. 00 0.02 0.05 R0 (kilo-ohm) 0.95 l. 00 1.02 1.05 Rn (kilo-ohm) 0. 475 0.500 0. 510 0. 525 Rm (kilo-ohm) 0. 2714 0.2857 0. 2914 0. 300

7 Sn 2.0 Sm 3. 5 Rp (kiloohm) 1.050 Rp (kilo-ohm) 0.00 fig (kilo-ohm) 20. 46 go (kilo-ohm) 1. 904 En (kilo-ohm) 1.462 1. 462 1.462 1. 462 Rm (kilo-ohm) 1.266 1. 266 1.266 1. 302 1. 302 1. 302 1. 504 1. 504 1. 504

then

In the above table, the definite values of F0, fin, and Tim have been verified by the following obvious equations:

and it is impossible to accomplish the desired three point compensation at any elaborate work of adjustment of V the thermistor deviations.

.circuit constants, because the Equation 7 is not satisfied as shown below.

Rn v

Thus, the upper permissible limit Rn(x) of the Rn should become smaller than the lower permissible limit Rn(N), and this, of course, is impossible.

Another design example of the present invention is given in Table II for maximum permissible deviation of 120% of thermistor resistance.

According to the Equation 11, is selected to be 0.65, and then 5:0.6894 13:0.03938 3'n=1.127 Tm==1.195 R0=3.195 kilo-ohm 'Rn=2.836 kilo-ohm Rm=2.674 kilo-ohm Table II Thermistor Deviation (Percent) -0. 20 0. 00 +0. 20 R0 (kilo-ohm) 0. 80 1. 00 l. 20 Rn (kilo-ohm) 0. 400 0. 500 0.600 Rm (kilo-ohm) o. 2286 0. 2857 0. 3429 Sn 2. 00 2.00 2. 00 Sm 3. 50 3. so a. s0 Rp (kilo-ohm) o. 00 1. 439 3. 000 Rp (kilo-ohm) 2. 451 1. 163 0. 00 En (kilo-ohm) 10. 90 12. 185 13. 35 3'0 (kiln-ohm) 3.195 3.195 3.195 in (kilo-ohm) 2. 835 2. 835 2. s35 Em (kilo-ohm) 2. 674 2. 674 2. 674 1.127 1.127 1.127

From the foregoing disclosures, it has been understood that the present invention provides a combination of a thermistor 1 and a resistor network 2 to be connected to a measuring instrument with energy source in cascade,

in which the resistances R0, Rn and Rm of the thermistor,

at three dilferent temperatures To, Tn and Tm, respectively, where To Tn Tm, and the corresponding resultant resistances E0, fin and Rm are so co-related that the resistance ratio functions 25 and ii satisfy the Equation 11, while the ratio Yin/Rn of resultant resistance to thermistor resistance at one temperature Tn satisfies the Equation 7, whereby the resultant resistances E0, fin and Tim can be maintained constant at the respective temperatures, in spite of certain deviations of the thermistor resistances, provided that the resistor elements of network 2 are selected or adjusted in proper manners in accordance with By this, thermistors are made interchangeable without necessity of re-adjustment of associated measuring instruments, and a Way to large scale production has been open for apparatus utilizing thermistors.

I claim as my invention:

1. In combination, a resistor network including series and parallel resistors-and a thermistor, in which (a) the resistance values R0, Rn and Rmof said thermistor at temperatures To, Tn and Tm, respectively, where To Tn Tm and the corresponding resultant resistances Tia, fin and Fm of said network with said thermistor have ratio values of substantially the following relations:

where 1.

and (b) the ratio value (Tin/Rn) of said resultant resistance to said thermistor resistance at one of said tem peratures, Tn, satisfies the following condition:

En (ti-x) 2. The combination according to claim 1, in which said resistor network comprises series and parallel resistances Rp, Rp and Rq, and has substantially definite resultant resistances F0, Tin and Tim at said temperatures To, Tn andTm, respectively, said resistances Rp, Rp and Rq being represented by substantially the following formulae:

where p=Rp/R0 O p' Rp/Ro 0 =Ro7Rq 3. A resistance network with thermistor, comprising a thermistor having resistancevalues R0, Rn and Rm at temperatures To, Tn and Tm, respectively, where and a resistor network having together with said thermistor different and definite resultant resistance values Tia, in

and Tim at said temperatures To, Tn and Tm, respectively, 1

irrespective of the deviation of said thermistor from its rated values of resistances, said resistor network com-.

4. In combination, a resistor network including series and parallel resistors and a thermistor, with a measuring 10 and (b) the ratio value (Rn/Rn) f said resultant instfument and mm source connected in a sistance to said thermistor resistance at one of said temwhich (a) the resistance values R0, Rn and km of said ventures, Tn, ti fi the f ll i condition: thermistor at temperatures To, Tn and Tm, respectively,

where T0 Tn Tm, and'the corresponding resultant re-' R 5 sistances fio, fin and fim of said network with said 15 (u 5)z 3 15 thermistor have ratio values of substantially the following relations: where u fi 5 x a when 2o '13=E-5 m- 1 References Cited in the file of this patent n=7o/ Rn( 1) 7 I UNITED STATES PATENTS sm=R0/Rm ;n) 2,086,910 Hansell July 13, 1937 2,567,755 Arnsler Sept. 11, 1951 2,567,756 Amsler Sept. 11, 1951 Sm-l 

